Formaldehyde $($CH$2$O$)$ can be produced industrially by partial oxidation with air over a silver catalyst. Suppose about $2/3$ mol formaldehyde is produced per $1$ mol methanol reacted and that, in addition, some formic acid, H$,$ CO$,$ and CO$2,$ are produced. In order to ensure high utilization of the reactant, the product gas is scrubbed with H$,$O to separate the off$-$gases. The residue is distilled to produce a pure recycle methanol. Assuming that the reactor inlet gas to the reactar is $35\%($mol$)$ methanol, calculate the moles of formaldehyde produced per mole of feed methanol, given the off$-$ gas composition $20\mathrm{.}2\%$ H$2,4\mathrm{.}8\%$ CO$2,0\mathrm{.}2\%$ CO$,74,5\%$ N$2,$ and $0\mathrm{.}3\%02.$ Please also give the degree of freedom analyisis and whether extent of reaction$/$atomic balance is being used to solve this question.